Theorem difeq1d 2161

Description: Deduction adding difference to the right in a class equality.

Hypothesis

Ref	Expression
difeq1d.1	|- (ph -> A = B)

Assertion

Ref	Expression
difeq1d	|- (ph -> (A \ C) = (B \ C))

Proof of Theorem difeq1d

Step	Hyp	Ref	Expression
1		difeq1d.1	. 2 |- (ph -> A = B)
2		difeq1 2156	. 2 |- (A = B -> (A \ C) = (B \ C))
3	1, 2	syl 10	1 |- (ph -> (A \ C) = (B \ C))

Syntax hints:   -> wi 3   = wceq 958   \ cdif 2047

This theorem is referenced by:  phplem4 4517  unfilem3 4562  alephsuc3 7587  cldval 7663  iscncl 7767  ishgrag 10740  hgralem 10741

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-dif 2052

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